Methods and systems for efficiently sampling portfolios for optimal underwriting

ABSTRACT

A method of valuation of large groups of assets by partial full underwriting, partial sample underwriting and inferred values of the remainder using an iterative and adaptive supervised and unsupervised statistical evaluation of all assets and statistical inferences drawn from the evaluation and applied to generate the inferred asset values. Individual asset values are developed and listed in relational tables so that individual asset values can be rapidly taken from the tables and quickly grouped in any desired or prescribed manner for bidding purposes. The assets are collected into a database, divided into categories by credit variable, subdivided by ratings as to those variables and then rated individually. The assets are then regrouped according to a bidding grouping and a collective valuations established by cumulating the individual valuations.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/173,957, filed Dec. 30, 1999, which is hereby incorporated byreference in its entirety.

BACKGROUND OF THE INVENTION

This invention relates generally to valuation methods for financialinstruments and more particularly to rapid valuation of large numbers offinancial instruments.

A large number of assets such as loans, e.g., ten thousand loans orother financial instruments, sometimes become available for sale due toeconomic conditions, the planned or unplanned divestiture of assets oras the result of legal remedies. The sale of thousands of commercialloans or other financial instruments sometimes involving the equivalentof billions of dollars in assets must sometimes occur within a fewmonths. Of course, the seller of assets wants to optimize the value ofthe portfolio, and will sometimes group the assets in “tranches.” Theterm “tranche” as used herein is not limited to foreign notes but alsoincludes assets and financial instrument groupings regardless of countryor jurisdiction.

Bidders may submit bids on all tranches, or on only some tranches. Inorder to win a tranche, a bidder typically must submit the highest bidfor that tranche. In connection with determining a bid amount to submiton a particular tranche, a bidder often will engage underwriters toevaluate as many assets as possible within a tranche and within theavailable limited time. When the time for submitting a bid is about toexpire, the bidder will evaluate the assets underwritten at that time,and then attempt to extrapolate a value to the assets that have not thenbeen analyzed by the underwriters.

As a result of this process, a bidder may significantly undervalue atranche and submit a bid that is not competitive or bid higher than theunderwritten value and assume unquantified risk. Of course, since theobjective is to win each tranche at a price that enables a bidder toearn a return, losing a tranche due to significant undervaluation of thetranche represents a lost opportunity. It would be desirable to providea system that facilitates accurate valuation of a large number offinancial instruments in a short period of time and understand theassociated probabilities of return for a given bid.

BRIEF SUMMARY OF THE INVENTION

In an exemplary embodiment, an iterative and adaptive approach isprovided wherein a portfolio is divided into three major valuations.Full underwriting of a first type of valuation of an asset portfolio isperformed based upon an adverse sample. A second valuation type isefficiently sampled from categories of common descriptive attributes,and the assets in the selective random sample are fully underwritten.The third valuation type is subjected to statistically inferredvaluation using underwriting values and variances of the first andsecond portions and applying statistical inference to individually valueeach asset in the third portion. Clustering and data reduction are usedin valuing the third portion.

As the process proceeds and more assets are underwritten, the number ofassets with values established in the first and second portions increaseand the number of assets in the third portion decreases and the varianceof the valuation of the assets in the third portion becomes more andmore defined. More specifically, the assets in the third portion areevaluated by grouping the assets into clusters having probability ofvalue based on similarity to valuations of assets in the first andsecond portions. At all times, there is a notation of value of theportfolio, but confidence in the valuation increases as the processprogresses. Hypothetical bids are generated using the valuations todetermine an optimum bid within parameters determined by the bidder. Theoptimum bid is identified through an iterative bid generation process.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram illustrating a known process for valuing aportfolio of assets;

FIG. 2 is a flow diagram illustrating valuing a portfolio of assets inaccordance with one embodiment of the present invention;

FIG. 3 is a flow diagram illustrating, in more detail, one embodiment ofa first portion of a rapid valuation process for large asset portfoliosthat breaks assets into categories of variance;

FIG. 4 is a flow diagram illustrating a second portion of a rapidvaluation process for a large asset portfolios that aggregates from abasis to a tranche or portfolio basis;

FIG. 5 illustrates a probability distribution for exemplary assets whoserecovery value is inferred;

FIG. 6 is a flow diagram of a supervised learning step of the process ofFIG. 3;

FIG. 7 is a flow diagram of an unsupervised learning step of the processof FIG. 3;

FIG. 8 is an embodiment of the process for unsupervised learning;

FIG. 9 is an embodiment of the generation 1 (first pass) rapid assetvaluation process;

FIG. 10 is a flow diagram of a fuzzy clustering method used in theunsupervised learning of FIG. 8;

FIG. 11 is a pair of tables showing an example of model selection andmodel weighting for a rapid asset evaluation process;

FIG. 12 is a table showing exemplary attributes for a rapid assetvaluation process; and

FIG. 13 is a cluster diagram of an exemplary clustering method for arapid asset valuation process; and

FIG. 14 is a computer network schematic.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is a diagram 10 illustrating a known process for valuing a largeportfolio of assets 12 through an underwriting cycle and through tomaking a bid for purchasing asset portfolio 12, for example, in anauction. FIG. 1 is a high level overview of a typical underwriting andextrapolation process 10 which is not iterative and not automated. Indiagram 10, underwriters underwrite 14 a number of individual assetsfrom portfolio 12 to generate an underwritten first portion 16 and anuntouched remainder portion 18. Before any of the assets areunderwritten, first portion 16 is zero percent and remainder portion 18is one hundred percent of portfolio 12. As the underwriting processprogresses, first portion 16 increases and remainder portion 18decreases. The objective is to underwrite as many assets as possiblebefore a bid is submitted for the purchase of asset portfolio. The teamof underwriters continues individually underwriting 14 until just beforea bid must be submitted. A gross extrapolation 20 is made to evaluateremainder portion 18. The extrapolated value 20 becomes thenon-underwritten inferred value 24. The gross extrapolation generates avaluation 24 for remainder portion 18. Valuation 22 is simply the totalof the individual asset values in first portion 16. However, valuation24 is a group valuation generated by extrapolation and may be discountedaccordingly. Valuations 22 and 24 are then totaled to produce theportfolio asset value 26. Valuation processes are performed on eachtranche of the portfolio.

FIG. 2 is a diagram illustrating one embodiment of a system 28 for rapidasset valuation. Included in FIG. 2 are representations of process stepstaken by system 28 in valuating asset portfolio 12. System 28individually evaluates (“touches”) every asset, except for a very smallquantity 30 of untouched assets considered statistically insignificantor financially immaterial. Specifically, all assets in portfolio 12other than quantity 30 undergo an iterative and adaptive valuation 32 inwhich the assets in portfolio 12 are individually valued, listedindividually in tables and then selected from the tables and groupedinto any desired or required groups or tranches for bidding purposes (asdescribed below.) As in diagram 10, underwriters begin a full underwrite14 of individual assets in portfolio 12 to produce a fully underwrittenfirst portion 16 of assets. Underwriters also underwrite 34 a sample ofassets in a second portion 36 of portfolio 12, and a computer 38statistically infers 40 value for a third portion 42 of portfolio 12.Computer 38 also repetitively generates 44 tables (described below)showing values assigned to the assets in portions 16, 36 and 42 asdescribed below. In one embodiment, computer 38 is configured as a standalone computer. In another embodiment, computer 38 is configured as aserver connected to at least one client system through a network (shownand described in FIG. 14), such as a wide-area network (WAN) or alocal-area network (LAN).

For example, and still referring to FIG. 2, an unsampled andnon-underwritten portion 46 of a third portion 42 of portfolio 12 issubjected to a statistical inference procedure 40 using fuzzy-C meansclustering (“FCM”) and a composite High/Expected/Low/Timing/Risk(“HELTR”) score to generate two categories 48 and 50. HELTR is definedas H—High cash flow, E—Expected cash flow, L—Low cash flow, T—Timing ofcash flow (for example in months: 0–6, 7–18, 19–36, 37–60), and R—Riskassessment of borrower (9—boxer used by credit analysts). Category 48 isdeemed to have sufficient commonality for evaluation as a whole.Category 50 is further divided into clusters 52 and 54 that are, inturn, further subdivided. Cluster 52 is divided into subclusters 56 and58, while cluster 54 is subdivided into subclusters 60, 62 and 64.Cluster and subclusters are shown both in a “tree” chart 66 and as boxesin valuation block 68. These individual asset values are then regroupedinto tranches 70, 72 and 74 for bid purposes. Any number of tranchescould be assembled in any arrangement set by the seller.

Individual asset data (not shown) for each asset in portfolio 12 isentered into a database 76 from which selected data 78 is retrievedbased on a given criteria 80 for the iterative and adaptive process 32.When criteria 80 is established for valuation of any asset, thatestablished criteria 80 is stored in database 76 for use in valuatingother asset data in database 76 which shares such an establishedcriteria. Iterative and adaptive valuation process 32 thus develops 82valuations (described below) and groups 84 them for use in bidding.

FIGS. 3 and 4 together form a flowchart 85 illustrating a functionaloverview of one embodiment of system 28 (shown in FIG. 2) for evaluationof a large asset portfolio 12. Valuation procedures 14, 34 and 40 (seealso FIG. 2) are simultaneously and sequentially used in system 28 in amanner described below. As described above, full underwriting 14 is afirst type of valuation procedure. Grouping and sampling underwriting 34with full underwriting of the samples is a second type of valuationprocedure. Statistical inference 40 is a third type of valuationprocedure, which is an automated grouping and automated valuation.Procedures 14, 34 and 40 are based on objective criteria established asdescribed below.

“Underwriting” as used herein means a process in which a person(“underwriter”) reviews an asset in accordance with establishedprinciples and determines a current purchase price for buying the asset.During underwriting, the underwriter uses pre-existing or establishedcriteria 80 for the valuations. “Criteria” means rules relevant to assetvalue and a rating based on such categories. For example, as a criteria,an underwriter might determine three years of cash flow history of theborrower to be a category of information relevant to asset valuation andmight give a certain rating to various levels of cash flow.

Full underwriting 14 is done in two ways, a full cash basis manner 86and a partial cash basis manner 88. Both full cash basis manner 86 andpartial cash basis manner 88 start with sets 90 and 92 of assets thatare fully individually reviewed 14 (see FIG. 2). Such full review 14 isusually due to the large dollar, or other appropriate currency, amountsof the assets being reviewed relative to other assets in the portfolioor due to the borrower being so well known or so reliable that theassets can be quickly and reliably fully underwritten or the assets aremarked to market such that there is very little variance associated withthe value of said assets. Asset set 90 is evaluated by underwriters 94and each asset in set 90 receives a valuation with very little variationsuch as an asset backed with cash or a tradable commodity with full cashvalue and is placed in a full value table 96. Selected individual valuesfor assets in table 96 are stored as a fully underwritten group value98.

Set 92 is evaluated by a team of underwriters 100, which could be thesame as team 94, but each asset receives a discounted or partial valueand is placed in a partial value table 102. Selected individual valuesfor assets in a tranche in table 102 are stored as a partial value fullyunderwritten group value 104. Criteria 80 (shown in FIG. 2) for fullcash basis manner 86 and partial cash basis manner 88 are stored indatabase 76 (shown in FIG. 2) in a digital storage memory (not shown) ofcomputer 38 (shown in FIG. 2) for use in supervised learning 206 andunsupervised learning 208 of automated valuation 40.

Sampling underwriting 34 is accomplished using two procedures, a fullsampling 106 procedure and a partial sampling 108 procedure. Fullsampling 106 is utilized for categories of large assets and includes aone hundred percent sampling 110 of the sample groups in the categoriesof assets being sampled. The assets in full sampling 106 are notindividually underwritten but rather are underwritten in full samplinggroups 112 based on a determined commonality. A resulting full samplinggroup valuation (not shown) is created and then desegregated based on arule 114 to generate an individual full sample asset value table 116.Individual full sample asset values in table 116 are then uploadedelectronically into any full sampling group valuation 118 required forbidding as suggested by the grouping of assets in a tranche. The numberof assets in an underwriting sample grouping can be as little as one toany number of assets. Partial sampling 108 is for medium categories ofassets and includes forming a cluster sample group 120 by one hundredpercent sampling of a representative group from within a cluster of thegroups being sampled and random sampling of the other groups in thecluster. In partial sampling 108, all groups are sampled, but some arepartly valued by extrapolation from cluster sample group 120. Partialsampling 108 includes an asset level re-underwrite 122 with manual dataentry 125 to produce an alpha credit analyst table 126 which is given anasset class adjustment 128 to produce an adjusted credit analyst table130. As described above, individual assets are selected from adjustedcredit analyst table 130 according to tranche grouping to produce apartial sampling credit value 132 for use in bidding on tranche 70(shown in FIG. 2).

Automatic valuation procedure 40 utilizes supervised learning process206, an unsupervised learning process 208 and an upload from astatistical inferencing algorithm 134 to generate an underwritingclusters table 136 which is stored in a digital storage device. Insupervised learning process 206, an experienced underwriter who knowswhat questions to ask to establish value, assists the computer indetermining whether or not an asset is a good investment and how tovalue the asset. In unsupervised learning process 208, the computersegments and classifies assets and objectively self-evaluates the assetsbased on feedback from the data. An underwriter periodically reviews theunsupervised learning process 208 to determine whether the computer ismaking sensible underwriting conclusions. The computer uses statisticalalgorithms 134 to make its inferences. For example, but not by way oflimitation, one embodiment uses the Design For Six Sigma (“DFSS”)quality paradigm developed and used by General Electric Company andapplied in a Due Diligence (“DD”) asset valuation process using amulti-generational product development (“MGPD”) mode to value the assetdata with increasing accuracy. Learning processes 206 and 208incorporate the accumulated knowledge as the valuation progresses intocash flow recovery and probability of recovery calculations on anongoing, real time basis. Supervised learning process 206 uses businessrules to identify clusters of assets having common aspects for valuationpurposes. Unsupervised learning process 208 uses feedback from priordata valuations performed by procedure 40 to determine if progress isbeing made with respect to increasing valuation confidence.Identification of all available raw data and discovery ofinterrelationships of clusters of these available raw data is possibledue to the use of high-speed computers, as is described below.

In one exemplary embodiment, a fuzzy clustering means (“FCM”) process ofunsupervised organization of raw data using a HELTR scoring technique isemployed to infer valuations of credit scores onto assets in portfolios,as described below. Such clustering techniques have been developed inresponse to more sophisticated classification segments to describeassets and high asset counts in portfolios that must be assessed in timeperiods that do not allow manual processing.

One exemplary method first organizes valuation scores (static and/orprobabilistic recoveries) in a computerized system. Adjustments are thenmade to the valuation scores for special factors and business decisions.Then a reconciliation of multiple valuation scores describing the sameasset and an overall adjustment to interview/override the inferredvaluation is performed.

Organizing valuation scores is performed by collating, in electronicform, a cluster number, a cluster name, descriptive attributes of thecluster(s), probabilistic recovery values (an illustrative example is aHELTR score) and the underwriter's confidence in each cluster'svaluation based upon the strengths of each cluster's descriptiveattributes. The cluster number is a unique identifier of a specific setof descriptive attributes that are facts about an asset which a personskilled in evaluations uses to assess value of an asset. Examples ofdescriptive attributes include, but are not limited to, payment status,asset type, borrower's credit worthiness expressed as a score, locationand seniority of a claim. The cluster name is, in one embodiment, analpha-numeric name that describes the cluster's descriptive attributesor sources. One example of descriptive attributes is found in FIG. 12,described below.

Descriptive attributes are the facts or dimensions or vectors that wereused to develop the asset's value. Computer logic is used to check forreplicated clusters, if any, and alert the analysts or underwriters.

Because each asset can be described by many combinations of descriptiveattributes, various levels of value for the same asset may occur.Probabilistic recovery values or credit score or any numericalindication of the asset's worth are indicators of worth designated atthe discrete asset level. All of the information from the variousdescriptive attributes is synthesized such that a purchase or sale pricecan be ascertained as a fixed value or a probabilistic one. Anillustrative embodiment used herein is the HELTR score. Each cluster hasa unique set of descriptive attributes and designated HELTR score.

Every cluster's unique attributes contribute to a valuation of clustervalue. Different combinations of attributes provide a higher confidenceor confidence interval of a particular cluster's score. For example, ifany asset was described as a green piece of paper with height equal to2.5″ and width equal to 5″—one might ascribe a value of 0 to 1000dollars and place very little confidence in this assessment. If thissame asset was described with one more fact or attribute or vector asbeing a real $20 US bill, one would place a very high confidence factoron this cluster value of $20 US dollars.

A cluster's valuation and confidence is determined at a point in timeand recorded. Sometimes new information becomes available and theanalyst would like to alter the value(s). The value is altered manuallyor automatically with a data field and decision rules, in the automatedfashion via computer code. The prior values are manipulated to reflectnew information. As an illustrative example, assume the prior clusterconfidence was recorded at 0.1 and it is learned that a different assetwith exact descriptive attributes as in this cluster just sold for overthe predicted “most probable” value. Rules were in effect such that ifthis event occurred, cluster confidence is multiplied by 10. 0.1×10=1which is the revised cluster confidence.

The purpose of such a process is to reconcile multiple scores for thesame asset, controlling for the confidence associated with each sourceof valuation of each dimension of valuation. Using the HELTR as anillustrative example with sample data points on a particular asset:

Cluster Cluster Valuative Number Name High Exp Low Time Confidence HighExp Low Time 1 Lien 85 62 .15 3  3 (3/1 65)(85) (3/1 65)(62) (3/165)(15) (3/1 65)(3) positions - recourse 2 Asset 45 4 31 3  7 (7/165)(45) (7/1 65)(4) (7/1 65)(31) (7/1 65)(3) classification - industry -age 3 Coordinates - 9 5 2 2 65 (65/1 65)(9) (65/1 65)(5) (65/1 54)(2)(65/1 65)(2) use - borrower n x  1 65 6999 4792 2374 2 6059

The cluster consensus valuation is a high value of 0.6999, most likely0.4792, low 0.2374 with a timing of 2.6059. Different logic can beapplied to manipulate any of the weights.

The consensus scores are developed in the context of global assumptions.Should a global assumption change occur, process steps 128, 138 areincluded in the methodology to weight the consensus score. Illustrativeexamples are fraud discovery in certain valuation factors, macroeconomicchanges, fungible market value established for an asset class, and lossof or increase of inferenced asset valuation methodologies relative toother methodologies being employed.

In another embodiment, a cross correlation tool is used to quicklyunderstand and describe the composition of a portfolio. Typically, thetool is used to correlate a response of a user selected variable versusother variables in an asset portfolio. The tool quickly identifiesunexpectedly high or low correlation between two attribute variables andthe response variable. Attribute variables are of two types, continuousand categorical. The cross correlations are computed by the correlationtool between all variables of interest and their bin or level andpresented, in one embodiment, in a two dimensional matrix for easyidentification of trends amongst the assets in the portfolios.

First, the cross-correlation tool identifies attribute variables in theportfolio of assets as one of continuous or categorical. For eachvariable aggregation levels are computed by bins for continuousvariables and by value for categorical variables.

A user looking to identify correlations with the tool will select aresponse variable, Y_(r), for example, an expected recovery or count.For all combinations of pairs of attribute variables (x1 and x2) andtheir levels (a and b), compute the average value of the responsevariable, Y_(r), according to:Y _(r)=sum(Y(x1=a and x2=b))/count(x1=a and x2=b).

An expected value, Y_(expect), of the response variable is calculatedaccording to:Y_(expect)=(sum(Y(x1=a))*count(x1=a)+sum(Y(x2=b))*count(x2=b)))/(count(x1=a)*count(x2=b)).

A deviation, Y_(error), of the chosen response variable, Y₁, from theexpected value, Y_(expect), using weighted values of occurrence of x1=aand x2=b separately, is calculated by:Y _(error) =Y _(r) −Y _(expect).

In one embodiment, expected values and deviations are displayed inmulti-dimensional displays to make variations from expected values easyto identify.

In another exemplary embodiment, a transfer function process thatconverts raw data into the ultimate bid price is used, as describedbelow. Table 136 is electronically adjusted using modified coefficientsdeveloped in procedures 14, 34 and 40 to give a coefficient adjustmentto a credit score 138 for the asset and to generate an adjusted creditanalyst table 140 of inferred individual asset credit values. Individualasset values are taken from table 140 as required by tranche grouping togenerate an inferred credit valuation 142. Finally an extrapolation ismade on the negligible remainder 30 of “untouched” assets to generate atable of untouched assets 144. Values from table 144 are selected togenerate an untouched asset valuation.

Full cash valuation 98, partial cash valuation 104, full sampling creditvaluation 118, partial credit values 132, inferred credit value 142 andany value assigned from untouched asset table 144 are cumulated and aremutually exclusive with the priority being full cash valuation 98 toinferred credit value 142 consecutively. A sum of the valuationsrepresents value of the portfolio.

FIG. 4 is a flow diagram of a bid preparation stage 168 performed bysystem 28 (shown in FIG. 2). The cumulated valuations 98, 104, 118, 132,142 and 144 are combined in a risk preference loan level valuation step146. A deterministic cash flow bridge 148 is produced using a cash flowtiming table 150 to develop a stochastic cash flow bridge 152. Astochastic or probabilistic cash flow bridge 152 is created and used todetermine a proposed tranche bid price 154 to which is applied a tranchemodel 156 iteratively until a certain threshold 158 is reached.Threshold 158 is, for example, an internal rate of return (“IRR”)greater than some value, a certain time to profit (“TTP”), and apositive net present value (“NPV”).

In general, NPV is defined as: $\begin{matrix}{{NPV} = {c_{0} + \frac{c_{1}}{1 + r}}} & \left( {{Equation}\mspace{14mu} A} \right)\end{matrix}$where C₀ is the investment at time 0, C₁ is the expected payoff at time1, and r is the discount factor. The basic idea is that a dollar todayis worth more than a dollar tomorrow.

In the case of insurance policies, NPV is defined as: $\begin{matrix}{{NPV} = {{\sum P} - {\sum E} - {\left( {\sum C} \right) \times \frac{A}{E_{W}}}}} & \left( {{Equation}\mspace{14mu} B} \right)\end{matrix}$where P is the premium, E is the expected nominal cost, and C is theclaim cost. In essence, Equation B is how net income as the differenceof profit and weighted expected risk is generated. Note that thesummation is summing across all the policies in a specific segment. Alsonote that all the premium, nominal cost, and claim cost have beendiscounted before entering the equation. As a result, a profitabilityscore is generated.

If threshold conditions 160 are met, bid 154 is subjected to a simulatedbid opening analysis 161 to predict whether the bid can be expected tobe a winning bid. An outcome of a sealed bid auction depends on sizes ofthe bids received from each bidder. Execution of the auction involvesopening all of the bids and selling the items up for auction to thehighest bidder. In traditional sealed bid auctions, bidders are notallowed to change their bids once their bid is submitted and bidders donot know the bids placed by other bidders until the bids are opened,making the outcome of the auction uncertain. By placing higher bids, aprobability that the auction will be won is higher, but value gain islower if it was possible to have won the auction at a lower price.

Simulating competitive bidding increases the probability of capturingthe highest upside of profitability by setting a range of bid/saleprices that have a propensity to exhaust any competing bidder's pursesbefore ones own purse such that the most desirable assets transact withthe highest preservation of capital. Pricing decisions are brought intofocus by an analytically robust process because pure anecdotal businessjudgment can be augmented by a data driven approach not subject to ahidden agenda, personality or unilateral knowledge.

Each potential bidder has a range of possible bids that might besubmitted to a sealed bid auction. The range of bids can be expressed asa statistical distribution. By stochastically sampling from adistribution of bid values, one possible auction scenario may besimulated. Further by using an iterative sampling technique, for examplea Monte Carlo analysis, many scenarios are simulated to produce adistribution of outcomes. The distribution of outcomes include aprobability of winning the auction item(s) and the value gain. Byvarying the value of ones own bid, a probability of winning the auctionagainst ones own bid price can be determined.

The following core elements are used to simulate a competitive biddingyield, codification of market rules and contracts into computerizedbusiness rules, codification of potential competition/market forces,forecasted budgets and priorities into a preference matrix, one's ownbidding capacity, preferences, risk/return tradeoffs agreed to codifiedinto a preference matrix, and a computerized stochastic optimization.

Analysis 160 simulates a competitive environment with other companieshaving various financial capabilities bidding against the bidscalculated by system 28. In one embodiment, analysis 160, for exampleand without limitation, includes a total bid limit such as would be thecase where the total value of the assets exceed the financialcapabilities of the entity using system 28. In one embodiment, analysis160 might assess the profitability, in such case of limited resources tobid, of bidding on various combinations of tranches. Analysis 160 alsotakes into account past history in bidding against known competitors andinformation on the various types of assets preferred by competingbidders. In analysis 160, the tranche bid is then evaluated and set bymanagement 162 and a final tranche bid 164 made. All valuations prior tothe making of the bid 164 can be repeated as desired. Further, since theprocess is self-adjusting and iterative, the tranche bid price 164 tendsto climb upward with each iteration as more and more value is found bythe iterations performed by system 28.

The process described by flowchart 85 includes an evaluation stage 166(shown in FIG. 3) and a bid preparation stage 168 (shown in FIG. 4).Evaluation stage 166 includes procedures 14, 34 and 40. Evaluation stage166 runs constantly until stopped, with the automatic valuationprocedure 40 and sampling procedures 34 attempting to find extra valuein various assets or categories of assets.

Referring once again to FIG. 2, and in accordance with rapid assetvaluation, data categories 170, 172 and 174 within the assets ofportfolio 12 are identified on each asset and stored in database 76.Iterative and adaptive valuation process 32 takes portions of selecteddata 78 and applies criteria 80 to the portions of selected data 78 in astatistical manner to increase the known asset value rather than theasset value being a gross extrapolation 20. In accordance with method 28the assets are divided into at least first portion 16, second portion 36and third portion or remainder 42. Using procedure 14, the assets inportion 16 are fully underwritten to determine valuation 98 and partialvalue fully underwritten valuation 104 and to establish criteria 80 forsuch valuation. Using procedure 34, process 28 samples a quantity ofassets from second portion 36 representative of groups in second portion36 to determine full sampling group valuation 118 and partial samplingcredit values 132 for second portion 36 and to establish additionalcriteria 80 for such valuation. Using procedure 40, partially supervisedlearning process 206 and partially unsupervised learning process 208 areperformed by an automated analyzer such as computer 38 of FIG. 2. Inorder to learn, the automated analyzer extracts established criteria 80and selected data 78 as to third portion or remainder 42 and dividesthird portion 42 into portions 46, and then further divides each portion46 into categories 48 and 50 and category 50 into clusters 52, 54 andclusters 52, 54 into subclusters 56, 58, 60, 62 and 64 using criteria 80imported from database 76 and each of processes 206 and 208. Individualasset valuations are established for the assets in subclusters 56, 58,60, 62 and 64 by statistical inference.

The individual asset valuations are listed in cluster tables 136 (seeFIG. 3) and after adjustment 138, listed in a credit analyst table 140.The established criteria 80 are objective since criteria 80 come fromdatabase 76 where they have been placed during full underwritingprocedure 14 and sample underwriting procedure 34. In other words,information obtained in full value table 96, partial value table 102,table 116, alpha credit analyst table 126, adjusted credit analyst table130, adjusted credit analyst table 140 and untouched asset table 144 forall assets is placed into database 76 in a digital storage device, suchas the hard disk storage 178 of computer 38, and correlations are madeby procedure 40 with criteria 80 from procedures 14 and 34. Duringprocedure 40, criteria 80 which are of statistical significance with anacceptable degree of reliability, are entered. That is, procedure 40iteratively learns as it values and establishes criteria 80. Supervisedlearning process 206 and unsupervised learning process 208 increase theaccuracy of statistically inferred valuation 142 by correlating toestablished criteria 80 in database 76 on assets in fully underwrittenfirst portion 16 and assets in sample underwritten second portion 36.Selected data 78 related to one or more assets in third portion 42similar to selected data 78 on assets in portions 16 and/or 36 arelocated in database 76 and then by statistical inference, a value foreach asset in third portion 42 is determined from the locatedinformation.

During the process described by flowchart 85, assets are valued at anindividual asset level, and the individual asset values are tabulated orgrouped in one or more combinations. To have maximum flexibility forvarious bidding scenarios, any subset of portfolio 12 is valued andpriced separately in a particular time frame. In known process 10, if aseller of assets regroups the assets, for example from groupings byasset company to groupings by geographical location of borrowers,revaluation of bids may be inadequate because gross extrapolation 20will need to be performed. In using system 28, because individual assetvalues are developed and listed in tables 96, 102, 116, 130, 140 and144, these values can be electronically regrouped into differentvaluations 98, 104, 118, 132, 142 whose “food chain” selection criteriais mutually exclusive and selectable by the analysts conducting theevaluation and is further described below. If the seller groups theassets, then grouping according to seller groups or tranches is easilymade and an appropriate valuation 146 developed for that tranche. Theindividual asset values are thus easily regrouped for third portion 42to objectively obtain an inferred valuation 142 for that group ortranche.

Many methods may be employed to establish asset value. Depending uponthe objectives of the valuation, the relative merits of differentvaluation methodologies establish the desirability of the valuationtechniques for a particular asset. One methodology is similar to a “foodchain” which preserves assumption development methods yet selects theintervals with the highest confidence intervals.

In one introductory illustrative example of a food chain, one may preferto value a financial asset more by what similar assets trade in the openmarket for versus an individual's opinion. In rank order, themarket-to-market value is selected over an individual's opinion.

In the same way assets in a portfolio with a forecasted cash flowrecovery may be evaluated by a number of valuation techniques. Thetypical objective is to establish, with as high a probability available,what the future cash flow will be. The valuation methodologies areranked in order of their capability to accurately quantify cash flow, orcash equivalent, forecasts with the least downside variances and/ormaximum upside variances. The asset is valued by all available methodsthat have merit, or may have business logic rules to eliminate duplicatework when it is known that more accurate methods will preclude the needto assess an asset's valuation once the best method has been employed.

In order to provide the best forecast of asset value, assets areevaluated by each method within a food chain until such time as they arevalued by the best available method for each particular asset. Once thisbest value is found, the asset is said to have its value, irrespectiveto other values lower (with more variance) in the food chain and is sentto the completed state.

As an example, a portfolio of assets is evaluated using a food chain.The first valuation method in the food chain is the one which mostclosely matches the valuation objectives—namely to find the value withthe highest degree of accuracy (tightest confidence interval). As soonas the asset is valued by a methodology for which a value wasestablished for that unique asset, it is sent to the valuation table andremoved from any further steps in the food chain. A list of assets fromthe original portfolio that did not match any valuation methods is keptin the untouched asset table. The objective is to drive this untouchedtable to zero assets.

One example of a food chain is as follows, in order of preference. (a)100% cash in hand for the asset, (b) partial cash in hand for the asset,(c) liquid market value for like asset, (d) direct underwrite, and (e)inferred underwrite.

The food chain approach provides an ability to find the best probabilitydistribution shape, reduces probability distribution variance(especially on the downside tails), provides capability to establishprobability distributions quickly while preserving all availableknowledge in the constituencies and provides the ability to provide thebest estimate of value at any point in the discovery process.

As shown in FIG. 4, the general framework of bid preparation stage 168is to price bid 164 similar to option valuation paradigms where thewinning investor will have the right, but not the obligation, to recoverthe investment. The values are desegregated into three parts for eachtranche, a time value of money component, an inherent value componentand a probable cash flow component. The time value of money and theinherent value are deterministically calculated and have littlevariation once established. The time value of money is computed bytaking a firm's cost of capital for a low risk investment multiplied bythe investment for the applicable period which represents an opportunityfor alternate investment that is foregone in order to make the presentinvestment. Inherent value is a known liquid asset value, which is inexcess of the purchase price and is available immediately after takingcontrol of the assets. One embodiment is a well traded securitypurchased below market value as part of a portfolio. Probable cash flowvariance is a function of the assumptions a due diligence team makes andthe process it selects to convert raw data into a cash flow recoverystream. The systems described herein are configured to reduce negativevariances and find value.

FIG. 5 is a triangular probability distribution graph for a typicalminimum three-point asset evaluation 180. In accordance with process 40a minimum of three cases per financial instrument are evaluated. Avertical axis 182 denotes increasing probability and a horizontal axis184 denotes increasing portion of recovery. A liquidation or worst casepercentage 186 of a face value line 188, a best case percentage 190 offace value 188, and a most probable case percentage and recovery value192 of face value 188 are shown. The probability of worse casepercentage 186 is zero, the probability of best case scenario 190 iszero and a probability 194 of the most probable percentage 192 ofrecovery is a value represented by point 196. The size of an area 198under a curve 200 defined by a line connecting points 186, 196 and 190is representative of value in the asset. The notational asset valueholds to an area 202 of a rectangle bounded by a 100 % probability line204 of a 100% recovery of face value 188 is a measure of the portion offace value 188 that can be attributed to the asset represented by curve200. Points 186, 196 and 190 and lines 188 and 204, and thus areas 198and 202, will vary depending on selected data 78 chosen for the asset inquestion and criteria 80 applied to the asset and ascribed probabilitiesof asset value recovery. Horizontal axis 184 can be expressed incurrency units (e.g. dollars) rather than percentage of face value. Whencurrency units are used, areas 198 under curves 200 for different assetswill be in currency units and thus areas 198 relate to each other inmagnitude and hence in significance to overall bids 70, 72 and 74. Themore that is known about the asset, the more curve 200 can be refined.Statistics are applied to curve 200 as criteria 80 are established tohelp establish the location of points 186, 196 and 190 and hence area198 and thus the expected value of the asset. The timing of cash flows,which affects value, can be based upon histogram results of the timingattributes.

For example, the cash flow recovery timing can be broken down into threebins of 0–6 months, 7–12 months, 13–18 months, and so on. The automatedanalyzer 38 using algorithm 134 can select the bin width based upon asensitivity study trade off of timing to valuation against the gaugerecovery and rate determined possible by an underwriter. In an exemplaryembodiment, a minimum of 4 bins should be utilized when the discountfactor is more than 25%. For a discount factor between 10 and 25, aminimum of 6 bins should be used to cover the likely recovery periods.

In accordance with procedure 40 other sources of data are chosen that anunderwriter would be able to utilize to assess value in a financialinstrument. Criteria 80, established by underwriting teams 94, 100 114,122 and 140 in procedures 14 and 34, are useful in that regard. Inaccordance with the process described by flowchart 85, raw data isturned into a recovery and a rule set is selected to apply a valuationto the raw data and this rule set is coded into the valuation databasein the form of criteria 80. Each time a cluster is touched by multiplehits during a valuation in procedures 14, 34 or 40, a consensus forecastis developed and applied to the cluster. In accordance with system 28,the probability distributions of cash flows and timing at the tranchelevel is determined by developing valuation transfer function 146 at theasset level which will take raw data, rationalize the assumptions thatdata will generate and aggregate the valuations of the individual assetsin the tranche.

Since all recoveries are not homogeneous, a method to establish thevariability of cash flow recoveries is provided. Individual assets areclustered by group exposure. As much face value as possible istraditionally underwritten in the time permitted, recognizing that asizable sample remains for clustering. Clustering reserves are estimatedusing a sample size equal to one hundred forty five plus 2.65% of theface count and a regression analysis of variance. This produces samplesizes of thirty for a face count of 100 assets, 150 for a face count of1,000 assets, 400 for a face count of 5,000 assets, 500 for a face countof 10,000 assets, and 600 for a face count of 20,000 assets.

During statistical inference procedure 40, assets remaining in thirdportion 42 of portfolio 12 are clustered by descriptive underwritingattributes or criteria 80 and random samples are taken from each clusterand the sample underwritten. In one embodiment, sampling from a clusterin procedure 40 is stopped when asset level mean variance falls below10%. In another embodiment, sampling is stopped when tranche level meanvariance falls below 15%. Portfolio mean variance is not used as a stoppoint if the potential unit of sale is less than the entire portfolio.In accordance with procedure 40, recovery valuation of the clustersampling is inferred onto the corresponding cluster population. In usingsystem 28, the goal is to touch each inferred asset valuation via threeor more unique clusters. During procedure 40 a cluster's underwritingconfidence and descriptive attribute's relevance is weighed.

By way of example, without limitation, 0=no confidence that thiscluster's descriptive attributes will provide a meaningful valuation;1=complete confidence that this cluster's descriptive attributes willprovide as accurate of a valuation as individually underwriting eachinstrument, and numbers between 1 and 0 indicate partial confidence inthe valuation. Reconciliation of these values occurs within adjustedcredit analyst table 130. In procedure 40 cash flow at asset level isthen adjusted by macroeconomic coefficients within adjusted creditanalyst table 140. Macroeconomic coefficients are, in one embodiment,associated with major asset classes such as for example, withoutlimitation, real-estate residential loan or commercial equipment loan.The coefficients can be globally applicable, such as by way of examplewithout limitation, legal climate, gross domestic product (“GDP”)forecast, guarantor climate, collections efficiency, borrower groupcodes, and the like.

One method for sampling a portfolio includes searching among key asset,borrower, and collateral characteristics for attributes which heavilyinfluence/generate risk. Table A below provides one example list ofportfolio attributes in an asset valuation scenario.

TABLE A Portfolio attributes Borrower Size (by Borrower Group UPB)Secured Syndicated (yes/no) Guaranteed Loan Type (Term, Revolving, etc.)% UPB from Liens in First Position Collection Score (0 = Bad, 1 = Good)12-month collections % of UPB % of Last Payment for Principal # BorrowerLoans Loan's portion of borrower UPB Single Family Residence ResidentialRetail Industrial Hospital Hospitality Multifamily LandDeveloped/Undeveloped/Other Office Stock/Margin Loans

Segmentation of the asset attributes is accomplished by encoding ofattributes into “dummy variables”. For example, a common asset attributeis “Has borrower made a payment in the last 12 months?”, which would beencoded in a variable as a “1” if the answer is yes, and “0” otherwise.Similar “dummy variables” are used for other asset attributes.

The segmentation procedure is completed by using any statisticalprocedure which process the encoded asset attributes in such a way so asto segment the portfolio into groups of similar assets. One suchalgorithm is K-means clustering. In an example, where three assetattributes, Unpaid Principal Balance (UPB), Probability of Payment, ascale from 0 to 1; and Secured Score, a probability of being secured byreal estate collateral are used, the assets might be classified intofive groups with similar attributes.

Once the groupings of assets is made, the number of samples to be takenand submitted for further underwriting review is calculated byestablishing the confidence level with which statements can be madeabout the total recoveries in each segment (k), establishing theprecision with which one wishes to estimate the total recoveries in eachsegment (h) and providing an a priori estimate of the level and range ofrecoveries as a percentage of total Unpaid Principal Balance (UPB) (R),according to:${{Var}\left( {\hat{Y}}_{R} \right)} = {{n\left\lbrack {1 - \frac{n}{N}} \right\rbrack} \times \frac{\left\lbrack {\sum\limits_{1}^{N}\; x_{i}} \right\rbrack^{2}}{\left\lbrack {\sum\limits_{1}^{n}\; x_{i}} \right\rbrack^{2}} \times \frac{\sum\limits_{1}^{N}\;\left( {y_{i} - {Rx}_{i}} \right)^{2}}{N - 1}}$

-   -   n=sample size    -   N=cluster size    -   x_(i)=UPB for sample i    -   y_(i)=recovery for sample i        $R = {\frac{\sum\limits_{1}^{N}\; y_{i}}{\sum\limits_{1}^{N}\; x_{i}} = {{cluster}\mspace{14mu}{expected}\mspace{14mu}{recovery}\mspace{14mu}\%}}$        $\begin{matrix}        {h^{2} = {k^{2} \times {n\left\lbrack {1 - \frac{n}{N}} \right\rbrack} \times \frac{\left\lbrack {\sum\limits_{1}^{N}\; x_{i}} \right\rbrack^{2}}{\left\lbrack {\sum\limits_{1}^{n}\; x_{i}} \right\rbrack^{2}} \times \frac{\sum\limits_{1}^{N}\;\left( {y_{i} - {Rx}_{i}} \right)^{2}}{N - 1}}} & \left( {{Equation}\mspace{14mu} C} \right)        \end{matrix}$        $h = {{{error}\mspace{14mu}{tolerance}\mspace{14mu}{for}\mspace{14mu}{estimating}\mspace{14mu} Y} = {\sum\limits_{1}^{N}\;{y_{i}\mspace{14mu}{with}\mspace{14mu}{\hat{Y}}_{R}}}}$        $\begin{matrix}        {{\hat{Y}}_{R} = {{\hat{R} \times {\sum\limits_{i = 1}^{N}\; x_{i}}} = {{\frac{\sum\limits_{i = 1}^{n}\; y_{i}}{\sum\limits_{i = 1}^{n}\; x_{i}} \times {\sum\limits_{i = 1}^{N}\; x_{i}}} = {\frac{\sum\limits_{i = 1}^{n}\;{\rho_{i}x_{i}}}{\sum\limits_{i = 1}^{n}\; x_{i}} \times {\sum\limits_{i = 1}^{N}\; x_{i}}}}}} & \left( {{Equation}\mspace{14mu} D} \right)        \end{matrix}$    -   k=constant in Tchebyshev's Formula:        ${{{\hat{Y}}_{R} - \mu_{{\hat{Y}}_{R}}}} \leq {k\sqrt{{Var}\left( {\hat{Y}}_{R} \right)}\mspace{14mu}{with}\mspace{14mu}{probability}} \geq {1 - \frac{1}{k^{2}}}$

By solving Equation C for n, required sample size for the given clusteris obtained. Solving Equation C further allows the user to state, withprobability $1 - \frac{1}{k^{2}}$the calculated sample size, n, and associated underwritten values willestimate the total cluster recoveries to within an error of h, assumingthat estimates of total segment recoveries are determined using EquationD.

In practice, it is difficult to estimate variability in total recoverieswithout available data. A spreadsheet tool implements the above bygenerating data in a Monte Carlo simulation, and guiding the userthrough an analysis of the results until a favorable sample size isderived.

Table B provides an example output from a study of a group of 20 loanswith estimated (expected) recoveries between 20% and 30% of UPB, and arange of UPB between 1 MM and 2 MM. Eight samples are needed to estimatethe total recoveries for the 20 loans to within 10% of actual, with 75%confidence.

TABLE B Sample Size Spreadsheet Wizard Sam- ple Cume Size Exp Rec ExpRec Cume UPS Exp Rec % Residual 1 779,131 779,131 2,936,279 26 5% — 2716,951 1,496,082 5,477,631 27 5% 27,259 3 359,327 1,855,409 6,702,09027 7% 12,042 4 481,798 2,337,206 8,538,875 27 4% (20,958) 5 606,7742,943,980 10,706,452 27 5% 10,750 6 418,899 3,362,880 12,207,495 27 5% 5,397 7 622,516 3,985,396 14,609,180 27 3% (32,665) 8 594,799 4,580,19516,911,278 27 1% (28,694) 9 713,922 5,294,117 19,440,132 27 2% 25,241 10494,230 5,788,346 21,153,615 27 4% 25,363 11 735,334 6,523,68024,031,814 27 1% (45,983) 12 683,155 7,206,835 26,387,193 27 3% 39,85713 748,413 7,955,248 29,256,251 27 2% (31,730) 14 419,885 8,375,13330,726,773 27 3% 19,068 15 757,050 9,132,183 33,682,971 27 1% (44,439)16 553,674 9,685,857 35,690,262 27 1%  8,922 17 761,579 10,447,43538,234,459 27 3% 66,386 18 677,811 11,125,246 40,756,944 27 3% (10,741)19 563,811 11,689,057 42,688,952 27 4% 34,790 20 434,763 12,123,82144,160,329 27 5% 30,810 Expected N (cluster size) n (sample size)Recovery % 20 6 27 5% Face Range ER % Range Face Value 2,000,000 5.0% 44160,329 Min Face Min ER % Expected Recovery 1,000,000 25.0% 12 123,821Confidence k Precision Precision % 75.0% 2 00 1 212,382 10.0%

The appropriate variance adjusted forecast is made for each asset andthe valuation tables are constructed to include every asset in theportfolio. The recovery is valued with continuous probabilities at theunit of sale, which in one embodiment is a tranche. In the use of system28, internal rate of return (“IRR”) and variance would then be assessed.Preferred tranches have lower variances for a given IRR. The probabilityof each tranche's net present value (“NPV”) to be above 0 is assessedusing the project's discount rate. A discount rate is determined fromthe opportunity cost of capital, plus FX swap cost, plus risks ingeneral uncertainties inherent in the variances of forecasted cash flowrecovery. If it appears that there is more than a five-percent certaintythat the project will have a negative NPV, no bid is made. Dealevaluation is by tranche with decision criteria being IRR, risk varianceof the IRR in a tranche, estimated willingness and ability of thetranche to pay, time to profit (“TPP”) and the risk variance in thepayback by tranche, and NPV of the expected cash flow by tranchediscounted to risk free rate.

In competitive bid circumstances when the content of asset portfolios isnot negotiable, the investor or seller has a strong financial incentiveto select only the portions of total assets available for transactionthat will give their aggregated financial structure the bestrisk/return. Meeting minimum risk/return expected values with assetsthat will have a higher probability of maximum upside probabilities iseven more attractive to investors.

The aggregated portfolio is divided into separately marketable subportfolios or tranches. Each tranch has a forecasted cash flowprobability distribution and time duration from prior analytics. Thesetranches are then given a trial price. The new assets are combined withthe existing asset performance of the selling or buying party andsubjected to Monte Carlo case generation (with associated crosscorrelations accounted for).

The tranch selection process includes a random selection of trances notto buy. Once the portfolio effects take on a pattern, the best selectionof tranches to purchase, at what price, subject to constraints is foundby stochastic optimization.

Using NPV can be misleading due to the effects associated with doublediscounting which will occur when pessimistic case scenarios arediscounted to obtain PV. Using time to profit is used to overcome thislimitation and the marginal capital cost or risk free rate is used inthe discounting as determined by analysts conducting the evaluation.

Supervised learning process 206 of inferred valuation procedure 40 andsteps 120, 122 and 126 of partial sampling procedure 108 havesubstantial similarity in that the underwriter is actively involved inthe process, but the process is automated. FIG. 6 is a flow diagramillustrating a process 210 for automated underwriting of segmentablefinancial instrument assets. First clusters of financial instruments aredefined 212 by common attributes. An expert opinion 214 of value isgiven for selected samples from the defined clusters based upon theattributes. This opinion is used in a sample underwriting process 216and values are checked for combinations of attributes and reconciled218. Process 210 then selects and sets 220 the individual attributes tobe used and then classifies 222 individual assets into clusters. Clustervaluation is applied 224 to each cluster asset. Using the clustervaluation, the values are desegregated by a rule 226 to create a creditanalyst table 228.

FIG. 7 is a flow diagram of one exemplary embodiment of unsupervisedlearning 208 that includes several modules. A data acquisition module230 collects relevant data 78 wherever available. A variable selectionmodule 232 identifies the asset relevant variables deemed critical bycredit review or with the most discriminate power in separating variousasset groups. A hierarchical segmentation module 234 segments the entireportfolio of assets into bins based on critical variables selected byanalysts. A FCM module 236 further classifies each bin into clustersbased on natural structure of the asset data. An underwriting reviewmodule 238 assigns projected cash flow and risk scores 138 (shown inFIG. 3) to each cluster. This score is then supplied to the individualasset values in credit analyst table 136 for the assets from theclusters being adjusted in procedure 40 to produce adjusted creditanalyst table 140. The process is iterative and continuous and can beperformed by computer so that it continues while standard underwritingis being performed elsewhere.

FIG. 8 illustrates an alternate exemplary inferred valuation process 240used in place of the process described in FIGS. 3 and 4. In alternateprocess 240, a seven-step process is used to rapidly value a real estateloan portfolio using a combination of full underwriting, partialunderwriting and inferred valuation. First, assets are sampled 242according to risk. Second, assets are underwritten 244, and valuationsrecorded. Third, market value clusters are formed 246, such as by FCM,as described below. Fourth, regression models are built 248, for theunderwritten assets. A best model is selected 250, for the underwrittenassets from among those built 248 earlier. Sixth, the counts for theselected models are calculated 252. Seventh, models are applied 254, asselected 250 to non-underwritten or inferentially valued portion 42 ofportfolio 12 in a manner weighted by the counts to predict individualvalues for each of the non-underwritten assets. The individual assetvalues produced according to process 240 are then placed in adjustedcredit analyst table 140 (see FIG. 3).

In sampling assets 242, underwriters use stratified random sampling toselect assets for detailed review. Strata are constructed fromcollateral attributes. Examples of collateral attributes for real estateportfolios include, collateral usage (commercial or residential),previous appraisal amount, market value cluster (predicted from previousappraisal amount, land area, building area, current appraisal amount,court auction realized price, property type and property location.Typically, assets are sampled in an adverse manner, i.e., purposelyselected from a list ordered by decreasing Unpaid Principal Balance(“UPB”) or Previous Appraisal Amount (“PAA”).

Underwriting 244 is a largely manual process in which expertunderwriters ascribe a notion of worth to collateral assets. Theunderwritten valuations are stored in a master database table, such asdatabase 76 (shown in FIG. 2). Valuations are typically summarized interms of monetary units (e.g., 100,000 KRW), at then current marketprices.

FIG. 9 is a high level overview 290 of the automated portion of theprocess employed by system 28. Automated procedures are used byunderwriters to assist in full underwriting based on procedure 34 (seealso FIG. 3). Knowledge captured in procedure 34 is applied in inferredvaluation procedure 40 to reduce cost and uncertainty in due diligencevaluations of financial instruments and to reduce cost and variabilitybetween due diligence valuations. The valuations are subjected to a cashflow model which includes asset level valuation 146, deterministic cashflow bridge 148, stochastic cash flow bridge 152 and cash flow table150. The resultant bid valuation 154 is subjected to gaming strategies160 and management adjustments 162 to produce the final bid 164.

FIG. 10 is a flow diagram of an exemplary embodiment of forming clusters246. In forming clusters 246, underwriters, with the aid of algorithms,such as for example algorithms 134 (shown in FIG. 3) perform an analysisusing a Classification And Regression Tree (“CART”) based model, whichresults in a grouping of UW assets by Collateral Usage and Market Value(“CUMV”) groups, using Previous Appraisal Amount (“PAA”) as the drivingvariable.

Two approaches to assess the performance of a CART based model areoutlined below. One approach utilizes a ratio of the sum of squarederror (SSE) of a CART based approach to that of a simple model, calledan error ratio. A simple model is a model which assigns an average assetprice to all assets. The second approach computes a coefficient ofdetermination, denoted as R², and defined asR ²=1−(SSE/SST), where SST is a sum of squares total.

R² is the contribution of a single asset within each segment relative tothe entire population, a higher R² value for an asset within aparticular segment, the higher is the contribution. The differentportfolio segments are ranked based on the two approaches giving anindication of how good the predictive capabilities of the model arewithin each portfolio segment, giving a comfort level to the bidder interms of pricing, for example, each tranche.

TABLE C Rank Error Ratios and R² value per asset Rank Error R-squared peRatio for Loan for C Tranche CO Data B C Grand Total C loans loans CO 01Sum of a Curr UPB THB 645,959,109 82,692,009 728,651,119 Count of LoanNo 66 10 76 Sum of SST 599,969,990,091,044 72,331,126,127,460672,301,116,218,504 Sum of SSE(CART) 252,008,256,587,36226,877,527,094,865 278,965,783,682,227 Sum of SSE(Simple)440,700,263,795,025 36,637,006,656,009 477,337,270,451,034 0.7336170.18% CO 02 Sum of a Curr UPB THB 58,779,400 379,765,147 438,544,547Count of Loan No 9 118 127 Sum of SST 32,332,549,696,1331,039,401,135,208,180 1,071,733,684,904,320 Sum of SSE(CART)6,139,933,273,655 83,849,226,818,428 89,989,160,092,064 Sum ofSSE(Simple) 7,037,799,486,368 136,366,441,963,041 143,404,241,449,4090.614882 0.06% CO 03 Sum of a Curr UPB THB 798,969,257 276,915,5731,075,884,830 Count of Loan No 98 99 197 Sum of SST2,869,807,879,172,670 1,017,087,163,438,760 3,886,895,042,611,430 Sum ofSSE(CART) 729,304,505,050,836 65,902,258,632,574 795,206,763,683,411 Sumof SSE(Simple) 929,822,648,064,552 41,730,444,375,417971,553,092,439,969 1.579237 0.46% CO 04 Sum of a Curr UPB THB916,281,888 184,828,399 1,101,110,287 Count of Loan No 116 28 144 Sum ofSST 927,232,177,539,735 223,991,862,418,471 1,151,224,039,958,210 Sum ofSSE(CART) 329,869,566,635,764 92,347,778,018,417 422,217,344,655,182 Sumof SSE(Simple) 688,543,329,448,792 62,722,788,782,158751,266,118,230,950 1.472316 0.11% CO 05 Sum of a Curr UPB THB221,769,281 41,505,412 263,274,692 Count of Loan No 36 19 55 Sum of SST270,033,444,922,605 164,601,058,694,452 434,634,503,617,058 Sum ofSSE(CART) 28,547,982,198,098 10,191,006,095,769 38,738,988,293,867 Sumof SSE(Simple) 28,897,015,065,918 8,519,509,247,449 37,416,524,313,3671.196196 0.14% Total Sum of a Curr 2,641,758,934 965,706,5403,607,465,475 UPB THB Total Count of Loan No 325 274 599 Total Sum ofSST 4,699,376,041,422,190 2,517,412,345,887,330 7,216,788,387,309,520Total Sum of 1,345,950,243,746,720 279,167,796,660,0541,625,118,040,406,770 SSE(CART) Total Sum of 2,095,001,055,860,660285,976,191,024,073 2,380,977,246,884,730 0.976192 0.22% SSE(Simple)R-squared (CART) 71 4% 88 9% 77 5% R-squared (Simple) 55 4% 88 6% 67 0%

A first step is to define relevant portfolio segmentations. Thesegmentations could be pre-defined tranches, for example, based onindustry, Unpaid Balance (UPB) amounts, region or customer risk. Table Cabove is an example of defined segments based on tranches and assetrankings (B or C).

Table C provides an example output from a study of a portfolio with fivetranches and two different asset types (B and C). The table shows howthe error ratio is ranked for the different segments. Also, the R²values for each asset are also computed for assets of type C within eachsegment.

A second step is to compute SSE values for each portfolio segment ofinterest for the CART model and for the simple model (extrapolation ofan average price). An error ratio is computed from the SSE based on theCART model divided by an SSE based on the simple model. If the errorratio is less than one, then the CART based model is a better predictorthan the simple model. As an added benefit, a superior model can beassembled as a “hybrid” combination of the CART and simple models, bychoosing the model which performs best in each segment, according to theerror ratio metric.

A third step is to compute R² values for each asset within eachportfolio segment. R² per asset is computed as (SST per segment−SSE persegment)/(overall SST for all assets×number of assets within eachsegment).

Lastly all the segments are ranked based on the error ratio computed inthe second step and the R² values computed in the third step. The modelis accurate in predicting price values for segments that rank high onboth of the two metrics, the error ratio and R² and superior models areassembled using these metrics.

Table D shows the relative ranking of the five tranches for the assetsof type C (from Table C) on the basis of the two performance metrics.

TABLE D Portfolio Segment Ranking Tranche CO C R-Squared Rank ErrorRatio Rank R-squared CO 01 0.73 0.18% 2 2 CO 02 0.61 0.06% 1 5 CO 031.58 0.46% 5 1 CO 04 1.47 0.11% 4 4 CO 05 1.20 0.14% 3 3

FIG. 10 is a flow diagram illustrating an exemplary embodiment offorming clusters 246 using FCM to choose clusters for modeling. Computer38 (shown in FIG. 2) forms clusters 246 by taking selected data 78 andperforming FCM analysis to produce the clusters.

FIG. 11 illustrates building models 248, selecting best models 250 andcalculating counts 252 in which six models are built using database 76.Computer 38 (shown in FIG. 3) performs this process. Model building 248is used to assist the underwriter in prioritizing assets for fullunderwriting 14 and sample-based underwriting 34, as well as forinferential valuation.

The lower portion of FIG. 11 is a table illustrating an exemplaryembodiment of selecting best models 250 from six models built inaccordance with building models 248 d. The models differ according towhich variables are used as X's. All models use CUMV Cluster (these arepresent for all assets). The models from building models 248 are used topredict Court Auction Value (“CAV”) 256 in addition to Market Value(“MAV”) 258. Other embodiments (not shown) use other models to predictother values

In selecting best models 250, the best models of K regression modelsunder consideration (here, K=6), are selected. The best model is chosenfor each UW asset, according to the following metric:${\min\limits_{k}\left\{ {{{abs}\left( {y - {\hat{y}}_{k}} \right)},{1E^{99}}} \right\}},$where y is the UW value to be predicted, and ŷ_(k) is a prediction fromthe k^(th) regression model, for k=1, 2, . . . , K.

In calculating counts 252, the number of times each of the K models isselected within each CUMV cluster is counted. FIG. 11 contains thesecounts for CAV and MAV modeling scenarios. Other modeling scenarios areused in other embodiments.

When applying models 254, the weighted average prediction from allmodels that yielded a prediction for each non-UW asset is used. Theweights are constructed from the frequencies of the counts calculated252, and the predictions come from the modeling process. In oneembodiment, a commercial statistical analysis software (SAS) system isused to produce the models. An artifact of using the SAS system is thateach non-UW asset will get a predicted UW value from each model forwhich the non-UW asset has each input variable, i.e., “X variable”present. Other modeling packages share this trait.) Equation E belowdetails the procedure. $\begin{matrix}{{\hat{\overset{\_}{y}}}_{l} = \frac{\sum\limits_{i,j,k}{I_{lk}f_{ijk}{\hat{y}}_{lk}}}{\sum\limits_{i,j,k}{I_{lk}f_{ijk}}}} & \left( {{Equation}\mspace{14mu} E} \right)\end{matrix}$

In Equation C, I_(lk)=1 if model k produced a prediction for asset l,and is zero otherwise; f_(ijk)=count of times model k was selected forUW assets among the i^(th) CUMV type (i=1,2), and the j^(th) CUMVcluster (j=1,2,3); and ŷ_(lk)=prediction for y_(l) from model k. Notethere is only a contribution from each modeling approach for which anasset has a prediction, with each being weighted by the number of timesthe modeling approach was selected for all UW assets of the same CUMVcluster.

Process 240 is also used to estimate a Lower Confidence Limit (“LCL”)and Upper Confidence Limit (“UCL”) for the mean prediction, with asubstitution of the corresponding statistic for ŷ_(lk) in Equation E.

Referring back again to FIG. 3, supervised learning process 206 andunsupervised learning process 208 use clustering. “Clustering” is a toolthat attempts to assess the relationships among patterns of the data setby organizing the patterns into groups or clusters such that patternswithin a cluster are more similar to each other than are patternsbelonging to different clusters. That is, the purpose of clustering isto distill natural groupings of data from a large data set, producing aconcise representation of a system's behavior. Unsupervised learningstep 208, employs a fuzzy clustering method (“FCM”) and knowledgeengineering to group assets automatically for valuation. FCM is a knownmethod that has been widely used and applied in statistical modeling.The method aims at minimizing intra-cluster distance and maximizinginter-cluster distance. Typically the Euclidean distance is used.

FCM 248 (see FIG. 10) at the same time minimizes the intra-clusterdistance and maximizes the inter-cluster distance. Typically theEuclidean distance is used. FCM is an iterative optimization algorithmthat minimizes the cost function $\begin{matrix}{J = {\sum\limits_{k = 1}^{n}\;{\sum\limits_{i = 1}^{c}\;{\mu_{ik}^{m}{{X_{k} - V_{i}}}^{2}}}}} & \left( {{Equation}\mspace{14mu} F} \right)\end{matrix}$where n is the number of data points; c is the number of clusters, X_(k)is the k^(th) data point; V_(i) is the i^(th) cluster centroid; μ_(ik)is the degree of membership of the k^(th) data in the i^(th) cluster; mis a constant greater than 1 (typically m=2). Note that μ_(ik) is a realnumber and bounded in [0,1]. μ_(ik)=1 means that i^(th) data isdefinitely in k^(th) cluster, while μ_(ik)=0 means that i^(th) data isdefinitely not in k^(th) cluster. If μ_(ik)=0.5, then it means thati^(th) data is partially in k^(th) cluster to the degree 0.5.Intuitively, the cost function would be minimized if each data pointbelongs exactly to a specific cluster and there is no partial degree ofmembership to any other clusters. That is, there is no ambiguity inassigning each data point to the cluster to which it belongs.

The degree of membership μ_(ik) is defined by $\begin{matrix}{\mu_{ik} = \frac{1}{\sum\limits_{j = 1}^{c}\;\left( \frac{{{X_{k} - V_{i}}}^{2}}{{{X_{k} - V_{j}}}^{2}} \right)^{\frac{1}{m - 1}}}} & \left( {{Equation}\mspace{14mu} G} \right)\end{matrix}$

Intuitively, μ_(ik) , the degree of membership of the data point X_(k)in the cluster centroid V_(i), increases as X_(k) is getting closer toV_(i). At the same time, μ_(ik) would get smaller as X_(k) is gettingfarther away V_(j) (other clusters).

The i^(th) cluster centroid V_(i) is defined by $\begin{matrix}{V_{i} = \frac{\sum\limits_{k = 1}^{n}\;{\left( \mu_{ik} \right)^{m}X_{k}}}{\sum\limits_{k = 1}^{n}\;\left( \mu_{ik} \right)^{m}}} & \left( {{Equation}\mspace{14mu} H} \right)\end{matrix}$

Intuitively, V_(i), the i^(th) cluster centroid, is the weighted sum ofthe coordinates of X_(k), where k is the number of data points.

Starting with a desired number of clusters c and an initial estimate foreach cluster center V_(i), i=1,2, . . . , c, FCM will converge to asolution for V_(i) that represents either a local minimum or a saddlepoint of the cost function. The quality of the FCM solution, like thatof most nonlinear optimization problems, depends strongly on the choiceof initial values—the number c and the initial cluster centroids V_(i)).

In one exemplary embodiment, the entire portfolio 12 is segmented byunsupervised fuzzy clustering and each cluster is reviewed byunder-writing experts. thereby assisting the underwriters in choosingthe financial instruments for full underwriting 14 and sampleunderwriting 34. Alternatively, this FCM can be applied just to portion42. As a result, each cluster gets assigned a HELTR composite score forpurposes of adjustment 138 (see FIG. 3) In essence, the HELTR compositescore captures both expected and range of cash flow, its timing and therisk associated with each cluster.

Referring now to FIG. 2, the ratio of full underwrite portion 16 to thetotal portfolio 12 is in one exemplary embodiment 25% of the assets and60% of the face value of all assets. Full underwriting of these assetsis warranted due to their size and value. However, this underwriting isfairly uniform for all underwriters, so the underwriting is not likelyto produce significant bidding variances. The remaining 40%, however,comprising portions 36 and 42, which in the exemplary embodimentconstitute 75% of the assets but only 40% of the face value are highlyspeculative until underwritten. To the extent value can be found inportions 36 and 42 f, for example without limitation, an additional fivepercent over gross extrapolation, the difference meaning the differencebetween winning and losing the entire portfolio bid or the entiretranche bid meaning hundreds of millions of dollars difference inprofit.

In the case of insurance policies, in accordance with procedure 40,statistics are used in an attempt to answer three basic questions: (a)How should we collect our data? (b) How should we summarize the data wecollected? And (c) How accurate are our data summaries? Algorithm 134answers question (c), and is a computer-based method without complicatedtheoretical proofs. Algorithm 134 for insurance policy inferentialvaluations is suitable for answering statistical inferences that are toocomplicated for traditional statistical analysis. Algorithm 134 forinsurance policy valuation simulates the distribution of statisticalestimates by repeatedly sampling with replacement. The algorithmgenerally is composed of three main steps: (I) Sampling withreplacement, (II) Evaluating statistics of interest, and (III)Estimating standard deviation.

In accordance with insurance algorithm 134, estimates of NPV standarderror are performed as follows. For each of the risk models and for eachsegment in the models, assuming there are N policies in the segment, nsamples are selected using sampling with replacement (for example,n=100). Each sample contains N policies, too, in this example. For eachsample, and for all historical policies: $\begin{matrix}{\frac{A}{E_{w}} = \frac{\sum({Act})}{\frac{\sum({Wtdexp})}{0\mspace{11mu} 72858}}} & \left( {{Equation}\mspace{14mu} I} \right)\end{matrix}$Next, net present value is generated by $\begin{matrix}{{NPV} = {{\sum P} - {\sum E} - {\left( {\sum C} \right) \times \frac{A}{E_{W}}}}} & \left( {{Equation}\mspace{14mu} J} \right)\end{matrix}$for recent policies. Compute the sample standard deviation for the n NPVvalues. In Equation I, Act is the actual claim and Wtdexp is theweighted expected claim for each individual policy.

FIG. 12 is a table of exemplary criteria 80 and exemplary rule sets forcredit scoring 138. Other criteria could be selected depending on thetype of financial instrument and particular bidding conditions or anyother desires or preferences of the bidder.

FIG. 13 is a more detailed tree chart diagram 260 similar to tree chart66 (see lower portion of FIG. 2). In FIG. 13, the segregation is by (a)whether secured, (b) whether revolving, (c) whether the last payment waszero. The result is six clusters 262, 264, 266, 268 270, 272, casuallyknown as a “shaker tree”.

FIG. 14 illustrates an exemplary system 300 in accordance with oneembodiment of the present invention. System 300 includes at least onecomputer configured as a server 302 and a plurality of other computers304 coupled to server 302 to form a network. In one embodiment,computers 304 are client systems including a web browser, and server 302is accessible to computers 304 via the Internet. In addition, server 302is a computer. Computers 304 are interconnected to the Internet throughmany interfaces including a network, such as a local area network (LAN)or a wide area network (WAN), dial-in-connections, cable modems andspecial high-speed ISDN lines. Computers 304 could be any device capableof interconnecting to the Internet including a web-based phone or otherweb-based connectable equipment, including wireless web and satellite.Server 302 includes a database server 306 connected to a centralizeddatabase 76 (also shown in FIG. 2) which contains data describing setsof asset portfolios. In one embodiment, centralized database 76 isstored on database server 306 and is accessed by users at one ofcomputers 304 by logging onto server sub-system 302 through one ofcomputers 304. In an alternative embodiment centralized database 76 isstored remotely from server 302. Server 302 is further configured toreceive and store information for the asset valuation methods describedabove.

While system 300 is described as a networked system, it is contemplatedthat the methods and algorithms described herein for examination andmanipulation of asset portfolios are capable of being implemented in astand-alone computer system that is not networked to other computers.

While the invention has been described in terms of various specificembodiments, those skilled in the art will recognize that the inventioncan be practiced with modification within the spirit and scope of theclaims.

1. A computer-implemented method for sampling assets in an asset portfolio for optimal underwriting coverage when only a portion of the assets are to be underwritten, said method implemented using a computer coupled to a database, said method comprising the steps of: determining descriptive attributes of assets in the portfolio; encoding individual attributes; clustering the assets for underwriting based upon occurrences of the descriptive attributes; and utilizing the computer to determine a number of samples to be submitted for further underwriting review by: establishing a confidence level regarding the total recoveries probable in each cluster of the portfolio, establishing a precision to which total recoveries in each cluster are estimated, and providing an estimate of a level and a range of recoveries as a percentage of total Unpaid Principal Balance (UPB).
 2. A method according to claim 1 wherein said step of establishing a confidence level regarding the total recoveries probable further comprises the step of determining a sample size, n, for the cluster of assets according to: $h^{2} = {k^{2} \times {n\left\lbrack {1 - \frac{n}{N}} \right\rbrack} \times \frac{\left\lbrack {\sum\limits_{1}^{N}\; x_{i}} \right\rbrack^{2}}{\left\lbrack {\sum\limits_{1}^{n}\; x_{i}} \right\rbrack^{2}} \times \frac{\sum\limits_{1}^{N}\;\left( {y_{i} - {Rx}_{i}} \right)^{2}}{N - 1}}$ h=desired precision n=sample size N=cluster size x_(i)=UPB for sample i y_(i)=recovery for sample i $R = {\frac{\sum\limits_{1}^{N}\; y_{i}}{\sum\limits_{1}^{N}\; x_{i}} = {{cluster}\mspace{14mu}{expected}\mspace{14mu}{recovery}\mspace{14mu}\%}}$ $h = {{{error}\mspace{14mu}{tolerance}\mspace{14mu}{for}\mspace{14mu}{estimating}\mspace{14mu} Y} = {\sum\limits_{1}^{N}\;{y_{i}\mspace{14mu}{with}\mspace{14mu}{\hat{Y}}_{R}}}}$ and solving for n.
 3. A method according to claim 2 wherein said step of providing an estimate of a level and a range of recoveries further comprises the step of estimating a level and range of recoveries according to: ${\hat{Y}}_{R} = {{\hat{R} \times {\sum\limits_{i = 1}^{N}\; x_{i}}} = {{\frac{\sum\limits_{i = 1}^{n}\; y_{i}}{\sum\limits_{i = 1}^{n}\; x_{i}} \times {\sum\limits_{i = 1}^{N}\; x_{i}}} = {\frac{\sum\limits_{i = 1}^{n}\;{\rho_{i}x_{i}}}{\sum\limits_{i = 1}^{n}\; x_{i}} \times {\sum\limits_{i = 1}^{N}\; x_{i}}}}}$ k=constant in Tchebyshev's Formula: ${{{\hat{Y}}_{R} - \mu_{{\hat{Y}}_{R}}}} \leq {k\sqrt{{Var}\left( {\hat{Y}}_{R} \right)}\mspace{14mu}{with}\mspace{14mu}{probability}} \geq {1 - {\frac{1}{k^{2}}.}}$
 4. A method according to claim 1 wherein said step of clustering the assets for underwriting further comprises the step of using a supervised clustering process to cluster the assets.
 5. A method according to claim 1 wherein said step of clustering the assets for underwriting further comprises the step of using an unsupervised clustering process to cluster the assets.
 6. A method according to claim 1 wherein said step of clustering the assets for underwriting further comprises the step of using a Monte Carlo process to cluster the assets.
 7. A system configured to sample assets in an asset portfolio for optimal underwriting coverage, said system comprising: a computer configured as a server and further configured with a database of asset portfolios and to enable valuation process analytics; at least one client system connected to said server through a network, said server further configured to: determine descriptive attributes of assets in the portfolio; encode individual attributes; cluster the assets for underwriting based upon occurrences of the descriptive attributes; and determine a number of samples to be submitted for further underwriting review by: establishing a confidence level regarding the total recoveries probable in each cluster of the portfolio, establishing a precision to which total recoveries in each cluster are estimated, and providing an estimate of a level and a range of recoveries as a percentage of total Unpaid Principal Balance (UPB).
 8. A system according to claim 7 wherein said server configured to determine a sample size, n, for the cluster of assets according to: $h^{2} = {k^{2} \times {n\left\lbrack {1 - \frac{n}{N}} \right\rbrack} \times \frac{\left\lbrack {\sum\limits_{1}^{N}\; x_{i}} \right\rbrack^{2}}{\left\lbrack {\sum\limits_{1}^{n}\; x_{i}} \right\rbrack^{2}} \times \frac{\sum\limits_{1}^{N}\;\left( {y_{i} - {Rx}_{i}} \right)^{2}}{N - 1}}$ h=desired precision n=sample size N=cluster size x_(i)=UPB for sample i y_(i)=recovery for sample i $R = {\frac{\sum\limits_{1}^{N}\; y_{i}}{\sum\limits_{1}^{N}\; x_{i}} = {{cluster}\mspace{14mu}{expected}\mspace{14mu}{recovery}\mspace{14mu}\%}}$ $h = {{{error}\mspace{14mu}{tolerance}\mspace{14mu}{for}\mspace{14mu}{estimating}\mspace{14mu} Y} = {\sum\limits_{1}^{N}\;{y_{i}\mspace{14mu}{with}\mspace{14mu}{\hat{Y}}_{R}}}}$ by solving for n.
 9. A system according to claim 8 wherein said server configured to estimate a level and range of recoveries according to: ${\hat{Y}}_{R} = {{\hat{R} \times {\sum\limits_{i = 1}^{N}\; x_{i}}} = {{\frac{\sum\limits_{i = 1}^{n}\; y_{i}}{\sum\limits_{i = 1}^{n}\; x_{i}} \times {\sum\limits_{i = 1}^{N}\; x_{i}}} = {\frac{\sum\limits_{i = 1}^{n}\;{\rho_{i}x_{i}}}{\sum\limits_{i = 1}^{n}\; x_{i}} \times {\sum\limits_{i = 1}^{N}\; x_{i}}}}}$ k=constant in Tchebyshev's Formula: ${{{\hat{Y}}_{R} - \mu_{{\hat{Y}}_{R}}}} \leq {k\sqrt{{Var}\left( {\hat{Y}}_{R} \right)}\mspace{14mu}{with}\mspace{14mu}{probability}} \geq {1 - {\frac{1}{k^{2}}.}}$
 10. A system according to claim 7 wherein said server configured to use a supervised clustering process to cluster the assets.
 11. A system according to claim 7 wherein said server configured to use an unsupervised clustering process to cluster the assets.
 12. A system according to claim 7 wherein said server configured to use a Monte Carlo process to cluster the assets.
 13. A computer for sampling assets in an asset portfolio for optimal underwriting coverage, said computer including a database of asset portfolios and valuation process analytics, said computer programmed to: determine descriptive attributes of assets in the portfolio; encode individual attributes; cluster the assets for underwriting based upon occurrences of the descriptive attributes; and determine a number of samples to be submitted for further underwriting review by: establishing a confidence level regarding total recoveries probable in each cluster of the portfolio, establishing a precision to which total recoveries in each cluster are estimated, and providing an estimate of a level and a range of recoveries as a percentage of total Unpaid Principal Balance (UPB).
 14. A computer according to claim 13 programmed to determine a sample size, n, for the cluster of assets according to: $h^{2} = {k^{2} \times {n\left\lbrack {1 - \frac{n}{N}} \right\rbrack} \times \frac{\left\lbrack {\sum\limits_{1}^{N}\; x_{i}} \right\rbrack^{2}}{\left\lbrack {\sum\limits_{1}^{n}\; x_{i}} \right\rbrack^{2}} \times \frac{\sum\limits_{1}^{N}\;\left( {y_{i} - {Rx}_{i}} \right)^{2}}{N - 1}}$ h=desired precision n=sample size N=cluster size x_(i)=UPB for sample i y_(i)=recovery for sample i $R = {\frac{\sum\limits_{1}^{N}\; y_{i}}{\sum\limits_{1}^{N}\; x_{i}} = {{cluster}\mspace{14mu}{expected}\mspace{14mu}{recovery}\mspace{14mu}\%}}$ $h = {{{error}\mspace{14mu}{tolerance}\mspace{14mu}{for}\mspace{14mu}{estimating}\mspace{14mu} Y} = {\sum\limits_{1}^{N}\;{y_{i}\mspace{14mu}{with}\mspace{14mu}{\hat{Y}}_{R}}}}$ by solving for n.
 15. A computer according to claim 14 programmed to estimate a level and range of recoveries according to: ${\hat{Y}}_{R} = {{\hat{R} \times {\sum\limits_{i = 1}^{N}\; x_{i}}} = {{\frac{\sum\limits_{i = 1}^{n}\; y_{i}}{\sum\limits_{i = 1}^{n}\; x_{i}} \times {\sum\limits_{i = 1}^{N}\; x_{i}}} = {\frac{\sum\limits_{i = 1}^{n}\;{\rho_{i}x_{i}}}{\sum\limits_{i = 1}^{n}\; x_{i}} \times {\sum\limits_{i = 1}^{N}\; x_{i}}}}}$ k=constant in Tchebyshev's Formula: ${{{\hat{Y}}_{R} - \mu_{{\hat{Y}}_{R}}}} \leq {k\sqrt{{Var}\left( {\hat{Y}}_{R} \right)}\mspace{14mu}{with}\mspace{14mu}{probability}} \geq {1 - {\frac{1}{k^{2}}.}}$
 16. A computer according to claim 13 programmed to use a supervised clustering process to cluster the assets.
 17. A computer according to claim 13 programmed to use an unsupervised clustering process to cluster the assets.
 18. A computer according to claim 13 programmed to use a Monte Carlo process to cluster the assets. 